Quantum Graphity models [1]}, [2]} are spin system toy models for emergent geometry and gravity. They are based on quantum, dynamical graphs whose adjacency is dynamical: their edges can be on (connected), off (disconnected),
or in a superposition of on and off. We can interpret
the graph as pregeometry (the connectivity of
the graph tells us who is neighbouring whom). A
particular graphity model is given by such graph states
evolving under a local Ising-type Hamiltonian. The graphity model of [2]}, for example, is a toy model for interacting matter and geometry,
a Bose-Hubbard model where the interactions are quantum variables.
